where \(R\)  stands for the Ricci scalar (curvature scalar), \(T\)  is the torsion scalar, \(Q\)  is the nonmetricity scalar and \({\cal T}\)  is trace of the energy-momentum tensor of matter Lagrangian \(L_{m}\) . The MG-VIII can be seen as some kind of unification of \(F(R), F(T), F(Q)\)  or \(F(R,{\cal T}), F(T, {\cal T}), F(Q, {\cal T})\)  theories (see [1]}, [2]}, [3]} respectively). For instance, if one imposes flatness (i.e. \(R^{\lambda }_{\;\;\alpha \mu \nu } \equiv 0\) ) and metric compatibility (\(Q_{\alpha \mu \nu }\equiv 0\) ) arrives at the \(f(T)\)  gravity [4]}, [5]}. Demanding flatness and a torsionless connection we get symmetric teleparallel \(f(Q)\)  gravity [6]}, [7]}. More generally, imposing only teleparallelism we arrive at the recently developed generalized teleparallel scheme of f(G) [8]}, [9]} theories. If no restriction on the connection is assumed then \((\ref {2.1})\)  serves as a specific generalization of metric-affine \(f(R)\)  gravity where where the energy momentum trace \(\cal T\)  and certain quadratic combinations of torsion and non-metricity are added as well. In fact in this generalized metric-affine setup one could consider also the presence of the hypermomentum analogue of the (metrical) energy momentum trace. Giving it a little thought we observe that similar to the trace \(\cal T\)  is the divergence of the dilation current as they appear in the trace of the canonicalHere \(t=t^{\mu \nu }g_{\mu \nu }\)  is the trace of the canonical energy momentum tensor \(t^{\mu \nu }\) . energy momentum tensor (see for instance [10]})
\(t={\cal T}+\frac{1}{2 \sqrt{-g}}\partial _{\nu }(\sqrt{-g}\Delta ^{\nu }) \;\;, \;\;\; \Delta ^{\nu }:=\Delta _{\mu }^{\;\;\mu \nu }\) 
